Locality and Monotonicity



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Locality and Monotonicity

Strictly speaking, neither the Laplace equation nor the biharmonic equation provides a local interpolation scheme. Depending on the topology of the grid point cloud, the change in any of the Dirichlet values may have an impact on all . The insertion of additional grid points also affects the values on grid points already present. The mutual influence (the coupling) of two points, however, does decay with increasing distance. The Laplace equation yields a monotonous interpolation scheme, whereas the biharmonic equation tends to produce ``overshoots'' at local maxima. For these reasons, both point-cloud interpolation methods are available in VORONOI and can be used alternatively to fit the requirements of the problem at hand.



Martin Stiftinger
Thu Oct 13 13:51:43 MET 1994